Necessary conditions for the correctness of the cauchy problem for operators with multiple char

DOI10.1080/03605309408821007zbMath0799.35162OpenAlexW2076882630MaRDI QIDQ4288029

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Publication date: 14 November 1994

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309408821007

zbMATH Keywords

\(C^ \infty\) well-posedness of the Cauchy problem

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80)

Cites Work

• Asymptotic solutions of oscillatory initial value problems
• Some remarks on the Cauchy problem
• The Cauchy problem for effectively hyperbolic equations (a special case)
• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• The Cauchy problem for effectively hyperbolic equations (a standard type)
• The Cauchy problem for hyperbolic equations with double characteristics
• Generalized Levi conditions for weakly hyperbolic equations. An attempt to treat the degeneracy with respect to the space variables
• Sur le problème de Cauchy pour une classe des opérateurs différentiels du type faiblement hyperbolique
• Fundamental solution for a hyperbolic equation with involutive characteristics of variable multiplicity
• An algebra of pseudo‐differential operators